It is necessary to find a trajectory in the three-dimensional space for a technical device (for example a robot). The path to be traveled on (trajectory) should be as short as possible and not lead to the technical device colliding with its environment. In addition to the pure geometric movement, further prespecifications for traveling on the path should be made by the trajectory. For example, the permissible speed range of the technical device has to be complied with at all times. In the case of robots, this means that, in the event of a movement of the end effector (for example a pair of welding tongs), the speed of the individual joints also has to lie below a technically prespecified maximum speed. In particular, singularities in the robot position have to be avoided and regions in the vicinity of a singularity have to be traveled through correspondingly slowly. Since, in future, robots will be used in flexible environments (for example industry 4.0 scenarios) and also the tasks to be implemented can vary (individualized production), it is increasingly difficult to check trajectories “manually” in respect of their feasibility.